Optical diffusers, photomasks and their methods of fabrication

ABSTRACT

A large mask with random apertures may be formed by forming a smaller mask (also called a cell mask) with a random pattern of transmissive apertures which is then repeatedly replicated to create the large mask. The random pattern may be created by perturbing the aperture locations by a small amount or the apertures may be randomly placed within the cell mask provided certain criteria are met. Alternatively, a large mask with a random pattern of transmissive apertures may be formed without using a cell mask. This large mask may be used to fabricate diffusers and other devices that do not suffer from the interference, diffraction and other optical effects common in devices having structures that are non-randomly patterned.

RELATED APPLICATIONS

This application is a divisional application of U.S. patent applicationSer. No. 11/489,715 (306.005), filed 20 Jul. 2006, now U.S. Pat. No.7,670,726 the contents of which are incorporated herein by reference inits entirety.

FIELD OF THE INVENTION

The present invention relates generally to optical diffusers, photomasksand their methods of manufacture, and more particularly, opticaldiffusers with randomly placed structures, photomasks with randomlyplaced apertures, and their methods of manufacture.

BACKGROUND

Photomasks may be used to fabricate optical diffusers and numerous otheroptical devices. Typically, most masks have apertures that are regularand very well ordered. However, the resultant optical devices oftensuffer from diffractive, interference, or other optical effects due tothe features produced by the mask being regular and very well ordered.Accordingly, there is a strong need in the art for devices and masksthat address these problems.

SUMMARY OF THE INVENTION

An aspect of the present invention is to provide a photomask including amask having a plurality of areas. Each of the plurality of areas has asubstantially identical pattern of transmissive apertures that arerandomly located.

Another aspect of the present invention is to provide method offabricating a photomask including selecting a transmissive aperturespattern by randomly generating transmissive apertures positions andforming the transmissive apertures pattern in a plurality of areas of amask.

Another aspect of the present invention is to provide an optical deviceincluding a device having at least one area with randomly located devicestructures on a substrate, each of the randomly located devicestructures has a bottom and a top. The bottom is between the top and thesubstrate, and cross-sections adjacent the tops of the randomly locateddevice structures have smaller areas than cross-sections adjacent thebottoms of the randomly located device structures. The randomly locateddevice structures are made from a transmissive polymerizable material.

Another aspect of the present invention is to provide a method offorming an optical device including selecting a transmissive aperturespattern by randomly generating transmissive apertures positions, andforming the transmissive apertures pattern in at least one area of amask, providing a layer of photopolymerizable material on a substrate,illuminating the mask with light to selectively photopolymerize thelayer of photopolymerizable material, and removing photopolymerizablematerial left unpolymerized after the illuminating the mask with lightsuch that the at least one area includes randomly located devicestructures on the substrate. Each of the randomly located devicestructures has a bottom and a top, and the bottom is between the top andthe substrate. Cross-sections adjacent the tops of the randomly locateddevice structures have smaller areas than cross-sections adjacent thebottoms of the randomly located device structures. Thephotopolymerizable material is transmissive after polymerization.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be described in detail with reference to thefollowing drawings in which like reference numerals refer to likeelements wherein:

FIG. 1 illustrates irradiation of a mixture of materials to formrandomly located structures;

FIG. 2 illustrates an exemplary diffuser according to the presentinvention;

FIG. 3 illustrates another exemplary diffuser that includes structureshaving a substantially light transmitting material overcoat;

FIG. 4 illustrates another exemplary diffuser similar to the diffuser ofFIG. 3 except that the substantially light transmitting materialovercoat also includes scattering particles;

FIG. 5 illustrates an exemplary liquid crystal display backlightincluding a diffuser according to the present invention;

FIG. 5A illustrates another exemplary liquid crystal display backlightincluding a diffuser according to the present invention;

FIG. 6 shows a photograph of a random pattern of circular apertures of aportion of a cell mask that do not overlap;

FIG. 7 shows a photograph of a random pattern of circular apertures of aportion of a cell mask that are allowed to overlap;

FIG. 8 shows a side view produced by a scanning electron microscope of adiffuser fabricated according to example 1;

FIG. 9 shows a top view produced by a scanning electron microscopefabricated according to example 1;

FIG. 10 shows a side view produced by a scanning electron microscope ofa diffuser fabricated according to example 2;

FIG. 11 shows a top view produced by a scanning electron microscopefabricated according to example 2;

FIG. 12 shows a side view produced by a scanning electron microscope ofa diffuser fabricated according to example 3;

FIG. 13 shows a top view produced by a scanning electron microscopefabricated according to example 3;

FIG. 14 shows a side view produced by a scanning electron microscope ofa diffuser fabricated according to example 4;

FIG. 15 shows a top view produced by a scanning electron microscopefabricated according to example 4;

FIG. 16 shows a side view produced by a scanning electron microscope ofa diffuser fabricated according to example 5;

FIG. 17 shows a top view produced by a scanning electron microscopefabricated according to example 5;

FIG. 18 shows a side view produced by a scanning electron microscope ofa diffuser fabricated according to example 6;

FIG. 19 shows a top view produced by a scanning electron microscopefabricated according to example 6;

FIG. 20 shows the measured angular distributions of exemplary diffuserswith wide FWHM angles fabricated according to examples 1 and 2;

FIG. 21 shows the measured angular distribution of exemplary diffuserswith narrower FWHM angles fabricated according to examples 5 and 6; and

FIG. 22 illustrates a 5 by 5 matrix of cell masks that make up a largemask.

DETAILED DESCRIPTION

Optical devices, such as diffusers, fabricated with features that arenot regular and very well ordered do not suffer from diffractive,interference, or other optical effects that impair their function as istypical when those features are regular and very well ordered. One wayto do this is to make the placement of the feature either not regular ornot very well ordered or both. A first way to accomplish this is tostart with a regular design and then randomly perturb the placement ofthe features. A second way to accomplish this is to randomly place thefeatures. A third way is to accomplish this is to generate a small areaas described in the first or second ways and then replicate that smallarea. For example, a large mask with random apertures may be formed byforming a smaller mask (also called a cell mask) with a random patternof transmissive apertures which is then repeatedly replicated in an XYstep and repeat pattern to create the large mask. This large mask may beused to fabricate diffusers and other devices that do not suffer fromthe interference and diffraction effects common in devices havingstructures that are non-randomly patterned. Furthermore, the large maskappears macroscopically uniform because the same random pattern isuniformly replicated over the area of the large mask and because theboundaries of a cell mask are checked with an algorithm to ensure thatsuitable separation between transmissive apertures will be maintainedwhen the cell mask is replicated.

The design process of a large mask begins with the selection of the cellmask size. This step may be skipped when the cell mask and the largemask are the same size. The cell mask must be large enough to preventthe appearance of a pattern in the large mask that can occur because theapertures inside a cell mask are random and thus not absolutely uniform.Thus, when the small cell mask is repeatedly replicated to cover thelarge mask area, the slight nonuniformities in the placement of theapertures of the cell mask that are not apparent can become apparent inthe large mask as some sort of pattern. It is this pattern in the largemask that can prevent the large mask from looking macroscopicallyuniform. To avoid the appearance of this pattern in the large mask, thecell mask size may be increased. Unfortunately, the design time andcomputer capacity also increases as the cell size increases.Accordingly, it has been found that cell mask sizes between 2 mm×2 mmand 20 mm×20 mm result in acceptable spatial uniformity in the largemask and may be designed with most personal or notebook computers in areasonable amount of time. Alternatively, a cell mask can have a shapeother than square.

Next, the shape, size and number of apertures in a cell mask areselected. Circular apertures generally result in an azimuthallysymmetric distribution of the optical devices made with the mask. Othershapes of aperture may also be used. The size of the apertures is mainlydetermined by the desired device performance and device fabricationprocesses. For example, the size of apertures in a cell mask may rangefrom 5 μm to 250 μm diameters with circular apertures. The number ofapertures in a mask for a given shape and size (density) is one of thedesign parameters to determine the angular distribution. The higher thenumber of apertures that do not overlap, the greater the scattering oflight with diffusers, hence a wider angular distribution. In some of therandomization methods detailed below, a minimum number of apertures maybe defined instead of a set number.

Next, a method of randomization is selected. One method is to use anon-randomly patterned aperture arrangement and perturb the locationsrandomly from the non-randomly patterned aperture arrangement locationsby a random amount that has some predetermined maximum amount. Themaximum perturbation distance may be determined by the size of theapertures, the distance between aperture center prior being perturbed,and the allowable amount of overlapping of apertures or the minimumseparation between apertures. The perturbation distance may have someminimum amount although this is not required. The direction ofperturbation may be in any random direction or may be in any othersuitable pattern.

A second method of randomization is to randomly place the centers of theapertures in the cell mask and make sure that there is at least acertain amount of separation between the aperture centers. Aperturecenters that do not have the desired separation are not included andanother random choice is made. The random choices are made until thecell mask has the specified number of apertures. Since the larger maskthat will be formed by a matrix of cell mask aperture patterns, theopposing boundaries (e.g., top/bottom, right/left) are checked for thedesired separation through an algorithm. This opposing boundary check ismade to ensure the macroscopic uniformity. Otherwise, the large maskand/or the device fabricated by the large mask may appear to have a gridpattern. The amount of separation may be such that apertures cannotoverlap each other or the amount of separation may be such that theapertures may overlap each other. The amount of separation needed tohave distinctive structures formed during device fabrication depends onthe size of the apertures and the particulars (e.g., collimation angle)of the UV system or other suitable system used to fabricate the device.The amount of light dispersion in diffusers increases as the number perunit area (density) of distinctive structures increases. When twostructures overlap, they form a single distinctive structure of largersize. Thus overlapping effectively reduces the density which allows morelight transmission in the normal direction and less being dispersed atnon-normal angles.

Alternatively, the apertures may include one or more types of apertures.For example, the apertures may be circular, elliptical, rectangular,pentagonal, hexagonal, octagonal, combinations of these shapes or anyother desired shape The orientation of a non-circular aperture may bedetermined randomly. If different types of apertures are used, thenumber of each may be random. Also, the cell mask may allow for wrappingof apertures from one border to the opposing border. In other words, ifan aperture is partly cut off due to the aperture being too close to theedge of the cell mask, that remaining part of that aperture is formed atthe opposing border such that when the cell mask is used to form thelarger mask, complete apertures are formed by two adjacent cell masks.

Any suitable method may be used to fabricate a device with a maskaccording to the present invention. For example, one exemplary method offabricating a diffuser with a mask with random aperture locations beginswith preparing a mixture of materials. The mixture of materials includesone or more components plus a photoinitiator or photoinitiators.Alternatively, the photoinitiator may be omitted if a photopolymerizablematerial is used that does not require a photoinitiator. The mixturealso may contain one or more non-photopolymerizable material componentssuch as solid particles, liquids, colloids, gases (e.g., air ornitrogen) or other useful components. The mixture should be uniformprior to photopolymerization. Next, as illustrated in FIG. 1, a carrierfilm 101 (which may also be called a substrate), such as a PET film, aPMMA film, a PVA film or any other suitable film, is placed upon aphotomask 103. The photomask 103 may have any suitable randomconfiguration. Additionally, an index matching fluid, such asisoproponol alcohol, may be applied between carrier film 101 and thephotomask 103. Next, a layer 102 of the mixture of materials is coatedonto the carrier film 101 through doctor blade coating, slot diecoating, or any other suitable coating techniques. The thickness of thelayer 102 may be between about 5 μm (0.2 mil) and about 508 μm (20 mils)with about 50.8 μm (2 mils) and about 254 μm (10 mils) being typical.

Next, as is illustrated in FIG. 1, a collimated or nearly collimated UVor visible light 104 passes through the transparent apertures of thephotomask 103 and selectively polymerizes the layer 102. The collimatedor nearly collimated UV or visible light 104 causes polymerization andthe formation of a solid structure. When phase separating materials areused, a first material of the layer 102 polymerizes to form the solidstructure while a second material (which is substantially different fromthe first material of the layer 102) phase separates from the firstmaterial during the irradiation of the collimated or nearly collimatedUV or visible light 104. The second material may be unpolymerizablematerial or material that does not polymerize from the collimated ornearly collimated UV or visible light 104. For example, the secondmaterial could be a thermally polymerizable material (e.g., athermopolymer) or any other polymerizable material that does notpolymerize as a result of irradiation of the collimated or nearlycollimated UV or visible light 104. If the second material ispolymerizable, this material may be polymerized after the removal of theunexposed areas of the layer 102. The second material also may be apolymerizable material that polymerizes from the irradiation of UV orvisible light. For example, the second material may polymerize at thesame or a substantially different rate from that of the first materialunder the irradiation of UV or visible light and is incompatible withfirst material after polymerization. The resultant structures,particularly the sides and/or tops are typically rough when phaseseparating materials are used and are typically smooth when non-phaseseparating materials or single component materials are used.

The mixture used in the layer 102 may include additional materials. Forexample, the first material could be a combination of two or morematerials and/or the second material could be a combination of two ormore materials. Also there could be two or more photoinitiators, orthere could be other materials such as a dye or pigment material in themixture. Furthermore, the mixture may be limited to inexpensivematerials as opposed to expensive materials (e.g., liquid crystalmaterials).

Next the selectively polymerized layer 102 is washed with solvent (e.g.,methanol, acetone, water, isopropanol or any other suitable solvent orsolvents) such that unexposed areas of the layer 102 are removed.Additionally, with phase separating materials, the second material inthe exposed areas of the layer 102 that are located at a boundarybetween an exposed area and an unexposed area are also removed becauseit is not fully surrounded by polymerized first material. This creates alight diffusing device structure 206 with rugged pitted surfaces insteadof smooth surfaces on the facets of the device structure 206. Furtherexamples of such diffusers may be found in U.S. patent application Ser.No. 11/439,437, which is incorporated herein in its entirety by thisreference. A plurality of these structures 206 forms an excellentdiffuser having a wide range of light diffusion angles. Similarlystructured diffusers may be fabricated using other fabrication methods.Such similarly structured diffusers may be made from phase separatedmaterials, may be made from non-phase separated materials or may be asingle material.

The device structure 206 formed with phase separating materials hasrugged pitted surfaces that provide multiple light scattering facets oneach structure 206. Some of these light scattering facets are parallelfacets 202 while others are inclined facets 204. The parallel facets202, which may be points, are generally parallel to the carrier film 101while the inclined facets 204 form an angle with carrier film 101between 0 and 90 degrees. However, the random nature and small size ofphase separation helps ensure a wide variation of facets which in turnhelps ensure a wide angle of light distribution. Additionally, bycontrolling the relative amounts of the first and second material in themixture, the relative amount of photoinitiator and/or the irradiation ofthe layer 102, the character (e.g., size, density, shape) of thesurfaces of the structure 206 may be selected. The ability to determinethe character of the surfaces allows one to select the angular lightdistribution characteristics of the resultant structures 206.

FIG. 3 illustrates another exemplary diffuser 300 that includesstructures 206 having a substantially light transmitting materialovercoat 302. The substantially light transmitting material overcoat 302has a different refractive index from the refractive index of thestructures 206. The greater the difference in refractive index, thewider the angular distribution of light. Typically, the refractive indexdifference is greater than about 0.005, with the refractive indexdifference often being greater than about 0.01. For example, thestructures 206 may be made from a mixture of ethoxylated (3) bisphenol Adiacrylate and polythylene glycol(600) diacrylate and have an averagedrefractive index of 1.52. The substantially light transmitting materialovercoat 302 may have a smaller refractive index (e.g., silicone,fluorinated acrylates or methacrylates, fluoro epoxies, fluorosilicones,or other such materials) or may have a larger refractive index (e.g.,polysulfone, polyphenylsulfone, polyethersulfone, or any other suitablematerials).

FIG. 4 illustrates another exemplary diffuser 400 similar to thediffuser 300 of FIG. 3 except that the diffuser 400 also includesscattering particles 402 in the substantially light transmittingmaterial overcoat 302. The scattering particles 402 may be glass beads,polymer (e.g., polystyrenes, acrylics, polycarbonates, olefins, or otheroptically clear polymer materials) particles, or particles of any othersuitable material.

The present invention may be incorporated into various kinds of lightsources and other devices. For example, FIG. 5 illustrates an exemplaryliquid crystal backlight (LCD backlight) 500 including a diffuseraccording to the present invention. A light source 502 emits light alongan edge of an optical waveguide plate 503. The light source 502 may becold cathode fluorescent lamps, light emitting diodes or any other lightsource. The light from the light source 502 is coupled into thewaveguide plate 503 and directed upwards by the waveguide plate 503. Theredirection of the light in the waveguide plate may be performed bystructured bottom surface of the waveguide plate 503, by printedscattering dots on a bottom surface of the waveguide plate 503 or by anyother means. Light coming out from a top surface of the waveguide plate503 typically lacks sufficient uniformity and has an undesired angulardistribution. Thus, diffusers and/or other optical elements are used toimprove the uniformity and reshape the angular distribution of thelight. For example, a first optical diffuser 504, a second opticaldiffuser 506, and an optical film 505 may be used. The optical film 505is used to further redirect light and may be a brightness enhancementfilm from 3M, the optical film described in U.S. Patent Application Ser.No. 60/677,837, which is incorporated herein by this reference, or anyother suitable film. Either one or both of the first and seconddiffusers 504, 506 may be a diffuser according to the present invention.Alternative numbers and types of films may be combined with one or morediffusers according to the present invention. Alternately, one or morediffusers may be used without any additional films.

FIG. 5A illustrates another exemplary liquid crystal backlight (LCDbacklight) 550 including a diffuser 551 according to the presentinvention. The LCD backlight 550 includes light sources 552 which may bean array of light emitting diodes (LEDs), cold cathode fluorescent light(CCFL) tubes or any other suitable light source which is located in acavity 553 of the LCD backlight 550. A LED is generally a point lightsource and CCFL tube is generally a linear light source. The spatialdistribution of light emitted from an array of LEDs or CCFL tubes isextremely non-uniform. A diffuser 551 according to present inventionhomogenizes the light emitted from an array of light sources 552 andmakes the light spatially uniform. Such an arrangement for LCD backlight550 may also be used for other purposes, such as general lighting.

FIG. 6 is a photograph of a random pattern of circular apertures of aportion of a cell mask that do not overlap. The transparent circularapertures are separated by a minimum of 4.2 μm between adjacent circleperipheries and the diameter of the transparent circular apertures is30.4 μm.

FIG. 7 is a photograph of a random pattern of circular apertures ofportion of a cell mask that are allowed to overlap. The centers ofadjacent transparent circular apertures are separated by greater than7.5 μm and the diameter of the transparent circular apertures is 28.1μm.

FIG. 8 shows a side view produced by a scanning electron microscope of adiffuser fabricated according to example 1. Substantial surface area ofthe inclined side facets and relatively small surface area of parallelfacets of a device structure are evidenced. In fact, the top surface ofa device structure is close to a point. As shown in FIG. 8, the surfacesof the facets are rough. FIG. 9 shows a top view produced by a scanningelectron microscope fabricated according to example 1. FIG. 10 shows aside view produced by a scanning electron microscope of a diffuserfabricated according to example 2. Part of device structures connectwith adjacent device structures, which is a result of small separationof the centers of transparent apertures in photomask. FIG. 11 shows atop view produced by a scanning electron microscope fabricated accordingto example 2. FIG. 12 shows a side view produced by a scanning electronmicroscope of a diffuser fabricated according to example 3. The glassbeads mixed with the photopolymerized materials are visible when theyreside on or very close to the surface of the device structures whilethe glass beads embedded inside the device structures are not visible.FIG. 13 shows a top view produced by a scanning electron microscopefabricated according to example 3. FIG. 14 shows a side view produced bya scanning electron microscope of a diffuser fabricated according toexample 4. These device structures have relatively large inclinedsurface areas and the surfaces are relative smooth. FIG. 15 shows a topview produced by a scanning electron microscope fabricated according toexample 4. FIG. 16 shows a side view produced by a scanning electronmicroscope of a diffuser fabricated according to example 5. These devicestructures have larger areas of parallel facets that result in adiffuser having a narrow angular distribution. FIG. 17 shows a top viewproduced by a scanning electron microscope fabricated according toexample 5. FIG. 18 shows a side view produced by a scanning electronmicroscope of a diffuser fabricated according to example 6. FIG. 19shows a top view produced by a scanning electron microscope fabricatedaccording to example 6.

As can be seen in FIG. 8 to FIG. 19, the randomly located devicestructures are substantially linked by the same material forming thedevice structures. The structures are not fully separated and defined attheir bottoms. This linkage helps prevent light leak which improves theperformance of the resultant diffusers.

FIG. 20 shows the measured angular distribution of two exemplarydiffusers with wide FWHM (Full Width Half Max) angles fabricatedaccording to examples 1 and 2. The vertical axis is normalized luminanceand the horizontal axis is the polar angle. The wide angulardistribution results from diffuser structures having small surface areaof parallel facets 202 and large surface area of inclined facets 204 asillustrated in FIG. 2. Exemplary diffuser structures are shown in FIG. 8through FIG. 15.

FIG. 21 shows the measured angular distribution of two exemplarydiffusers with narrower FWHM (Full Width Half Max) angles fabricatedaccording to examples 5 and 6. The vertical axis is normalized luminanceand the horizontal axis is the polar angle. The angular distributionresults from diffuser structures having relatively larger area ofparallel facets 202 as illustrated in FIG. 2.

The data shown in FIG. 20 and FIG. 21 are taken by using an EZContrast160D ELDIM measurement system from ELDIM S. A., France. Collimated whitelight incidents onto the diffuser from substrate side and diffused lightis collected and analyzed by the ELDIM measurement system.

FIG. 22 illustrates a 5 by 5 matrix of cell masks 2202 that make up afabrication mask 2200. The large mask 2200 may be formed by a step andrepeat process (e.g., an XY step and repeat process) with the cell mask2202 or any other suitable process.

Example 1

A mixture containing 15.0 w.t. % of monomer ethoxylated (6)trimethylolpropane triacrylate¹, 19.5 w.t. % of metallic acrylate esteroligomer¹, 44.0 w.t. % of Sartomer low viscosity oligomer¹, 19.5 w.t. %of urethane acrylate oligomer¹, and 2.0 w.t. % of2,2-dimethoxy-1,2-diphenylethan-1-one² was prepared using a compressedair mixer. The mixture was then degassed using ˜10⁻¹ torr vacuum toremove air bubbles before coating. A PET substrate³ having a 7 milthickness was cleaned by blowing it with ionized air. The mixture wascoated onto the substrate using a doctor blade to a wet thickness of 8.5mil (˜215 μm). A mask including the pattern of FIG. 6 was placedadjacent the substrate and a UV dosage of 75 mJ/cm² of ultraviolet lightfrom a metal arc lamp having a collimation angle ˜1.5° was used toilluminate the coating through the photomask. The UV exposed coating(with substrate) is then submerged in an agitated methanol bath forabout 25 seconds to remove unpolymerized monomer. The substrate and thepolymerized monomer are dried by blowing off any remaining solvent.Finally a post cure was performed by irradiating 608 mJ/cm² of UVdosage.

Example 2

A mixture containing 15.0 w.t. % of monomer ethoxylated (6)trimethylolpropane triacrylate¹, 19.5 w.t. % of metallic acrylate esteroligomer¹, 44.0 w.t. % of Sartomer low viscosity oligomer¹, 19.5 w.t. %of urethane acrylate oligomer¹, and 2.0 w.t. % of2,2-dimethoxy-1,2-diphenylethan-1-one² was prepared using compressed airmixer. The mixture was then degassed using ˜10⁻¹ torr vacuum to removeair bubbles before coating. A PET substrate³ having a 7 mil thicknesswas blown with ionized air to clean the PET film. The mixture was coatedonto the PET using a doctor blade to a wet thickness of 8.5 mil (˜215μm). A mask including the pattern of FIG. 7 was placed adjacent thesubstrate and a 75 mJ/cm² of ultraviolet light from a metal arc lamphaving a collimation angle ˜1.5° was used to illuminate the coatingthrough the photomask. The UV exposed coating (with substrate) is thensubmerged in an agitated methanol bath for about 25 seconds to removeunpolymerized monomer. The substrate and the polymerized monomer aredried by blowing off any remaining solvent. Finally a post cure wasperformed by irradiating 606 mJ/cm² of UV dosage.

Example 3

A mixture containing 44.3 w.t. % of monomer ethoxylated (3) bisphenol Adiacrylate¹, 44.3 w.t. % of monomer polythylene glycol(600) diacrylate¹,8.9 w.t. % of metallic acrylate ester oligomer¹, 0.5% of glass beads(with diameters between 3 to 5 μm) and 2 w.t. % of photoinitiator2,2-dimethoxy-1,2-diphenylethan-1-one (benzyl dimethyl ketal)² wasprepared using compressed air mixer. The mixture was then degassed using˜10⁻¹ torr vacuum to remove air bubbles before coating. A PET substrate³having a 7 mil thickness was blown with ionized air to clean the PETfilm. The mixture was coated onto the PET using a doctor blade to a wetthickness of 8.5 mil (˜215 μm). A mask including the pattern of FIG. 6was placed adjacent the substrate and a UV dosage of 55 mJ/cm² ofultraviolet light from a metal arc lamp having a collimation angle ˜1.5°was used to illuminate the coating through the photomask. The UV exposedcoating (with substrate) is then submerged in an agitated methanol bathfor about 25 seconds to remove unpolymerized monomer. The substrate andthe polymerized monomer are dried by blowing off any remaining solvent.Finally a post cure was performed by irradiating 607 mJ/cm² of UVdosage.

Example 4

A mixture containing 98 w.t. % of monomer ethoxylated (6)trimethylolpropane triacrylate¹ and 2 w.t. % of photoinitiator2,2-dimethoxy-1,2-diphenylethan-1-one (benzyl dimethyl ketal) wasprepared using compressed air mixer. The mixture was then degassed using˜10⁻¹ torr vacuum to remove air bubbles before coating. A PET substrate³having a 7 mil thickness was blown with ionized air to clean the PETfilm. The mixture was coated onto the PET using a doctor blade to a wetthickness of 8.5 mil (˜215 μm). A mask including the pattern of FIG. 6was placed adjacent the substrate and a UV dosage of 75 mJ/cm² ofultraviolet light from a metal arc lamp having a collimation angle ˜1.5°was used to illuminate the coating through the photomask. The UV exposedcoating (with substrate) is then submerged in an agitated methanol bathfor about 25 seconds to remove unpolymerized monomer. The substrate andthe polymerized monomer are dried by blowing off any remaining solvent.Finally a post cure was performed by irradiating 608 mJ/cm² of UVdosage.

Example 5

A mixture containing 89.8 w.t. % of monomer ethoxylated (6)trimethylolpropane triacrylate¹ and 9.0 w.t. % of difunctional aminecoinitiator¹, 0.3 w.t. % of photoinitiator1-hydroxy-cyclohexyl-phenyl-ketone² and 1.0 w.t. % of photoinitiator2,4,6-trimethylbenzoyl-diphenyl-phosphineoxide² was prepared usingcompressed air mixer. The mixture was then degassed using ˜10^(˜1) torrvacuum to remove air bubbles before coating. A PET substrate³ having a 7mil thickness was blown with ionized air to clean the PET film. Themixture was coated onto the PET using a doctor blade to a wet thicknessof 8.5 mil (˜215 μm). A mask including the pattern of FIG. 6 was placedadjacent the substrate and a UV dosage of 55 mJ/cm² of ultraviolet lightfrom a metal arc lamp having a collimation angle ˜1.5° was used toilluminate the coating through the photomask. The UV exposed coating(with substrate) is then submerged in an agitated methanol bath forabout 25 seconds to remove unpolymerized monomer. The substrate and thepolymerized monomer are dried by blowing off any remaining solvent.Finally a post cure was performed by irradiating 609 mJ/cm² of UVdosage.

Example 6

A mixture containing 13.4 w.t. % of monomer ethoxylated (6)trimethylolpropane triacrylate¹, 17.9 w.t. % of metallic acrylate esteroligomer¹, 40.6 w.t. % of Sartomer low viscosity oligomer¹, 17.9 w.t. %of urethane acrylate oligomer¹ and 8.9 w.t. % of difunctional aminecoinitiator¹, 0.3 w.t. % of photoinitiator1-hydroxy-cyclohexyl-phenyl-ketone² and 1.0 w.t. % of photoinitiator2,4,6-trimethylbenzoyl-diphenyl-phosphineoxide² was prepared usingcompressed air mixer. The mixture was then degassed using ˜10⁻¹ torrvacuum to remove air bubbles before coating. A PET substrate³ having a 7mil thickness was blown with ionized air to clean the PET film. Themixture was coated onto the PET using a doctor blade to a wet thicknessof 8.5 mil (˜215 μm). A mask including the pattern of FIG. 6 was placedadjacent the substrate and a UV dosage of 55 mJ/cm² of ultraviolet lightfrom a metal arc lamp having a collimation angle ˜1.5° was used toilluminate the coating through the photomask. The UV exposed coating(with substrate) is then submerged in an agitated methanol bath forabout 25 seconds to remove unpolymerized monomer. The substrate and thepolymerized monomer are dried by blowing off any remaining solvent.Finally a post cure was performed by irradiating 607 mJ/cm² of UVdosage.

¹Suitable materials may be obtained from the Sartomer Company of Exton,Pa. ²Suitable materials may be obtained from the Ciba SpecialtyChemicals of Tarrytown, N.Y. ³Suitable substrates may be obtained fromTekra of Orange, Calif.

The transmissive polymerizable material may be formed from a singlematerial or may be formed from a mixture of two or more materials. Thetransmissive polymerizable material may include photopolymerizablematerial and non-photopolymerizable material. For example, thephotopolymerizable material may be photopolymerizable monomers, dimmersor any other suitable material or combination of photopolymerizablematerials while the non-photopolymerizable material may be selected fromsolids, solid particles, liquids, colloids, gases (e.g., air ornitrogen) or combinations of these materials. The transmissivepolymerizable material may include one or more photoinitiators.

Although certain materials have been used in the above examples, itshould be understood that any suitable materials may be used. Also, itshould be understood that endless variations of large random masks andrandom cell masks may be created and that the mask examples areexemplary.

Although several embodiments of the present invention and its advantageshave been described in detail, it should be understood that changes,substitutions, transformations, modifications, variations, permutationsand alterations may be made therein without departing from the teachingsof the present invention, the spirit and the scope of the inventionbeing set forth by the appended claims.

1. A method of forming an optical device comprising: selecting atransmissive apertures pattern by generating a plurality of cell maskareas, the cell mask areas disposed in an XY matrix, all of the cellmask areas having a substantially identical pattern of transmissiveaperture locations; forming transmissive apertures, corresponding to thetransmissive apertures pattern, in a mask; providing a layer ofphotopolymerizable material on a substrate; illuminating the mask withlight to selectively photopolymerize the layer of photopolymerizablematerial; and removing photopolymerizable material left unpolymerizedafter the illuminating the mask with light such that the substrateincludes device structures corresponding to the transmissive apertures;wherein each of the device structures has a bottom and a top, whereinthe bottom is between the top and the substrate, wherein cross-sectionsadjacent the tops of the device structures have smaller areas thancross-sections adjacent the bottoms of the device structures, whereinthe photopolymerizable material is transmissive after polymerization,and wherein the device structures, viewed over the substrate as a whole,appears randomly placed and macroscopically uniform without an apparentgrid pattern.
 2. The method according to claim 1, wherein the step ofselecting a transmissive apertures pattern by generating a plurality ofcell mask areas is performed such that, within each of the plurality ofcell mask areas, the transmissive aperture locations correspond to apattern of locations which are perturbed from a non-random pattern oflocations at each location in a random direction and by a randomdistance where the random distance is no more than a maximum distance.3. The method according to claim 2, wherein the step of selecting atransmissive apertures pattern by generating a plurality of cell maskareas is further performed such that the transmissive aperture locationsare separated from each other by at least a minimum distance.
 4. Themethod according to claim 3, wherein the minimum distance is selectedsuch that adjacent device structures can overlap each other.
 5. Themethod according to claim 3, wherein the minimum distance is selectedsuch that adjacent device structures cannot overlap each other.
 6. Themethod according to claim 1, wherein each of the device structures hassmooth sides or a smooth top.
 7. The method according to claim 1,wherein each of the device structures further has rough sides or a roughtop.
 8. The method according to claim 1, wherein the top of each of thedevice structures is a point.
 9. The method according to claim 1,wherein the layer of photopolymerizable material is formed from a singlematerial.
 10. The method according to claim 1, wherein the layer ofphotopolymerizable material is formed from a mixture of two or morematerials.
 11. The method according to claim 10, wherein the layer ofphotopolymerizable material includes photopolymerizable material andnon-photopolymerizable material.
 12. The method according to claim 11,wherein the non-photopolymerizable material is selected from one or moreof the group consisting of: solids, solid particles, liquids, colloids,and gases.
 13. The method according to claim 12, wherein the gases areeither air or nitrogen.
 14. The method according to claim 1, wherein thedevice structures diffuse light.
 15. The method according to claim 3,wherein after the step of selecting a transmissive apertures pattern bygenerating a plurality of cell mask areas, the method further comprisesthe step of: a) removing, from a cell mask area, a transmissive aperturelocation spaced less than the minimum distance from transmissiveaperture locations in adjacent cell mask areas and any opposing cellmask areas.
 16. The method according to claim 15, further comprising thesteps of: adding a randomly placed transmissive aperture location to thecell mask area having a transmissive aperture location removed in stepa); and repeating step a); wherein the added transmission aperturelocation is separated at least the minimum distance from othertransmissive aperture locations in the cell mask area.